The length , breadth and height of a cuboidal shaped box of medicine is 20 cm , 12 cm and 10 cm respectively . Find the total surface area of the box .

Answer

To find the total surface area (TSA) of a cuboidal box, we will use the formula for the total surface area of a cuboid:

**Formula:**
\[ \text{TSA} = 2(LB + BH + HL) \]

Where:
- \( L \) = Length of the cuboid
- \( B \) = Breadth of the cuboid
- \( H \) = Height of the cuboid

**Given:**
- Length \( L = 20 \, \text{cm} \)
- Breadth \( B = 12 \, \text{cm} \)
- Height \( H = 10 \, \text{cm} \)

**Step 1: Calculate the products of the dimensions.**
1. Calculate \( LB \):
\[ LB = 20 \, \text{cm} \times 12 \, \text{cm} = 240 \, \text{cm}^2 \]

2. Calculate \( BH \):
\[ BH = 12 \, \text{cm} \times 10 \, \text{cm} = 120 \, \text{cm}^2 \]

3. Calculate \( HL \):
\[ HL = 10 \, \text{cm} \times 20 \, \text{cm} = 200 \, \text{cm}^2 \]

**Step 2: Add the products together.**
\[ LB + BH + HL = 240 \, \text{cm}^2 + 120 \, \text{cm}^2 + 200 \, \text{cm}^2 \]
\[ = 240 + 120 + 200 = 560 \, \text{cm}^2 \]

**Step 3: Multiply the sum by 2 to find the total surface area.**
\[ \text{TSA} = 2 \times (LB + BH + HL) \]
\[ \text{TSA} = 2 \times 560 \, \text{cm}^2 = 1120 \, \text{cm}^2 \]

**Final Answer:**
The total surface area of the cuboidal box is \( 1120 \, \text{cm}^2 \).

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